The statement in the text
The weight of the batter has very little to do with the matter of home runs, but his arm muscles are a controlling factor to the extent of, say, fifty percent. Of course, if his arms are rigid enough to make the bat for all practical purposes a part of his body when he hits the ball, and if his body is swung forward at just that instant, it is possible that a heavy batter, all other things being equal, would be able to knock the ball farther than a lighter player.
The batter's job is to get the bat in the right place at the right time with as high a speed as possible. To do that, he needs to supply energy from his body and transfer that energy efficiently to the bat. It seems reasonable to me that the weight of a batter, especially the weight contained in muscle, is relevant for the amount of energy that the batter can supply to the bat. Moreover, the arm muscle probably plays only a small role in obtaining bat speed. It is mainly the large muscles of the thighs and chest that supply most of the energy. The arms merely serve as a sort of delivery mechanism, to transfer the energy to the bat.
The author seems to think that with rigid arms, the weight of the batter himself contributes to the weight of the bat, so that a heavier batter can hit the ball harder than a lighter batter. This is almost surely not the case, as I have discussed at great length elsewhere and as first pointed out by Prof. Howard Brody. In a seminal article, Brody reported the results of his experiments and concludes the article with the following quote:
"...the concept of adding some fraction of the hand and arm mass to the bat mass to get an effective mass or striking mass seems to be contradicted by the results presented in this article."
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